Remark 3 As discussed in Section , the ICG routine given in Algorithm  is a deterministic method with the estimated gradient \(z_k\)  in (REF ). The number of iterations, \(t_k\) , required to run Algorithm  is given by \(t_k = \lceil \sqrt{k}\rceil \) . That is, we require more precise solutions for the ICG routine, only for later outer iterations. Furthermore, due to the deterministic nature of the ICG routine, further advances in the analysis of deterministic conditional gradient methods under additional assumptions on the constraint set \(\mathcal {X}\)  (see, for example, [1]}, [2]}) could be leveraged to improve the overall LMO complexity.

